Question

Of all rectangles with a perimeter of 29, which one has the maximum area? (Give the dimensions) The rectangle that has the maximum area has length ___ and width __.

Answer 1

Answer:

Both length and width of 7.25m

Step-by-step explanation:

Let L and W be the length and width of the rectangle, respectively. Since the perimeter is 29, we have the following equation

(L + W)2 = 29

L + W = 29/2 = 14.5

L = 14.5 - W

Also the area of the rectangle would be as the following:

A = LW = W(14.5 - W) = 14.5W - W^2

To find the maximum area possible, we can take the first derivative and set it to 0

A' = 14.5 - 2W = 0

2W = 14.5

W = 14.5 / 2 = 7.25m

L = 14.5 - W = 14.5 - 7.25 = 7.25m